Subgroups — #13114981

Order 1664.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#376	C₂	1	1	yes	maximal, characteristic
2	#11718116	C₂	1	6	yes	maximal
3	C₂×C₄²×C₁₃	C₂²	1	3	yes	—
4	C₂²×#1055	C₂²	1	4	yes	—
5	C₁₃×#95	C₄	1	4	yes	—
6	C₂²×C₄×C₁₃	C₂×C₄	1	6	yes	—
7	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
8	C₄²×C₁₃	—	2	6	no	—
9	C₂×#1055	—	2	12	no	—
10	#1840	—	13	1	no	maximal, Sylow
11	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₃	—	2	6	no	—
13	C₂×C₄×C₁₃	—	2	12	no	—
14	C₂×C₄×C₁₃	#41	1	6	yes	—
15	#1055	—	4	4	no	—
16	#376	D₁₃	1	1	yes	characteristic
17	#336	—	13	6	no	—
18	C₂²×C₁₃	#117	1	3	yes	—
19	C₂²×C₁₃	#131	1	4	yes	—
20	C₄×C₁₃	—	4	6	no	—
21	C₄×C₁₃	#126	1	4	yes	—
22	C₂²×C₈	—	13	4	no	—
23	C₂×C₄²	C₂×D₁₃	1	3	yes	—
24	#95	Dic₁₃	1	4	yes	—
25	C₂×C₁₃	#383	1	1	yes	characteristic
26	C₂×C₁₃	#433	1	6	yes	—
27	C₂²×C₄	C₂×Dic₁₃	1	6	yes	—
28	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
29	C₂×C₈	—	26	12	no	—
30	C₄²	—	2	6	no	—
31	C₁₃	#1840	1	1	yes	characteristic, complemented, Sylow
32	C₂³	C₂²×Dic₁₃	1	1	yes	characteristic
33	C₂×C₄	—	2	6	no	—
34	C₂×C₄	—	2	12	no	—
35	C₂×C₄	#6127	1	6	yes	—
36	C₈	—	52	4	no	—
37	C₂²	#88180	1	3	yes	—
38	C₂²	#88202	1	4	yes	—
39	C₄	—	4	6	no	—
40	C₄	#88130	1	4	yes	—
41	C₂	#11718598	1	1	yes	characteristic
42	C₂	#11718661	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₃
commutator, socle, prime radical	C₂³×C₁₃	C₂²×C₄
Fitting	C₁₃×#376	C₂
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	#376	D₁₃
hypocenter	C₁₃	#1840
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
31. C₁₃	#1840	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.